Computing with Quantum Cats (29 page)

Neutrons and protons are both so-called “spin-½” particles. This means that they can exist in either of two spin states, +½ or –½, also known as “up” and “down,” which can be equivalent, as we have seen, to 0 and 1 in binary code. You might think that this would mean that the overall spin of a nucleus of silicon-28 would be anything up to 14, depending on how the spins of individual nucleons add up or cancel out; but the quantum world doesn't work like that. Instead, each pair of protons aligns so that the spins cancel out, and the same is true for each pair of neutrons. So nuclei with even numbers of both protons and neutrons have zero overall spin, but other nuclei have non-zero spin. Thus silicon-28 has zero spin, but silicon-29 has an overall spin of ±½. This is what makes pure silicon-28 such a perfect background material against which to monitor the spins of atoms used to dope the crystal lattice.

NMR, though, doesn't use nuclei as complicated as those of silicon-28. It depends on the fact that there is an interaction between magnetism and nuclear spin, so that applying the right kind of alternating magnetic field to a nucleus can make it jump between energy levels corresponding to different spin states. This is the resonance in nuclear
magnetic resonance, and it shows up as an absorption of energy at a precise frequency of oscillation, the resonance frequency. The simplest nucleus to work with is the hydrogen nucleus, which is a single proton. The exact response of the proton to the oscillating magnetic field depends on its chemical environment—which molecules the hydrogen atoms are part of—so by sweeping a varying magnetic field across the human body and measuring the resonance at different locations it is possible to get a map which reveals the chemical environment of the hydrogen atoms in different parts of the body. That's what we know as an MRI scan.

The curious feature of quantum computing using NMR, though, is that we are dealing not with individual spins, but with some kind of average of billions and billions of essentially identical states—typically involving 10
²⁰
nuclei. In a fluid
¹⁴
being used for quantum computation in this way, the energy difference between the two spin states of the proton is very small, and this means that although nuclei prefer to be in the lower energy level, it is easy for them to get knocked up into the upper level by random interactions (literally, by neighbor atoms bumping into them). Once there, they will fall back down again; but meanwhile, other nuclei have been bumped up to take their place. At any one time, for every million nuclei in the upper level there may be only a million and one in the lower energy level. In effect, the NMR computing technique is working with the one in a million “surplus” nuclei in the lower level, getting them to jump up to the higher level. But it is working with
all
of them at once. And all of those “one in a million” nuclei, billions of them, jumping together between energy levels, have to be regarded as a single qubit, switching between the states 0 and 1.

I explained in the
previous chapter
how effective the technique has been in demonstrating the techniques of quantum computing with small numbers of qubits (up to 10 or so). But as I also mentioned, there are severe scaling problems with the technique, and it has already been pushed about as far as it can go. Even so, it isn't quite ready to be consigned to the dustbin of history. There is something very odd about NMR computation, which has set people thinking along completely different lines—as I shall discuss in the Coda.

Meanwhile, another old warhorse of a quantum computation technique, the ion trap approach, which
is
scalable, has quietly made steady progress. This was recognized in 2012 by the award of a half-share of the Nobel Prize in physics to David Wineland, of NIST, whom we met in
Chapter 5
.

TRAPPED IONS TAKE A BOW

Wineland's Nobel citation specified that the award was for “ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems.” In the words of the Royal Swedish Academy of Sciences, which administers the awards, if the quantum computer is built in the near future it “will change our everyday lives in this century in the same radical way as the classical computer did in the last century.” In this connection, there is one important feature of the ion trap approach which should be borne in mind when considering all the possibilities for computing with quanta. It is the only method in which all of the physics involved uses standard techniques that have all been tried and tested and proven to work. Every one of the other approaches, even though they are based on sound theoretical principles, relies on there being some kind of
practical physics breakthrough in the not too distant future if they are to maintain momentum. So while one or another of them may seem to spurt ahead for a time, like the fabled hare, so far they have each ground to a halt after a while, while the trapped ion technique continues to plod along, tortoise-like, improving the technology but always using the same physics.
¹⁵
Winfried Hensinger says that the first working quantum computer, in about the middle of the 2020s, is likely to be based on the trapped ion technique, and to be as big as a house. But you only have to compare the size of Colossus with the size of a modern smartphone to realize that this will be far from the end of the story.

Wineland has helped the trapped ion tortoise to take a few more steps down that road. Born in Milwaukee, Wisconsin, on February 24, 1944, he moved to California as a child and attended high school in Sacramento. He took his first degree at the University of California, Berkeley, graduating in 1965, received his PhD from Harvard in 1970, and worked at the University of Washington in Hans Dehmelt's group before joining the National Bureau of Standards in 1975. One focus of his work with trapped ions there has been towards the development of more accurate clocks—better timekeeping devices than the atomic clocks which are now standard. In 1979 Wineland founded the ion storage group of the Bureau, now based at NIST in Boulder, Colorado, using the techniques which I described in the
previous chapter
.

As I have explained, the problem with developing the trapped ion technique into a practical quantum computer is that it is extremely difficult to control strings of trapped ions containing more than about 20 qubits. Wineland and his colleagues have proposed getting around this difficulty by
dividing the “quantum hardware” up into chunks, carrying out calculations using short chains of ions that are shuffled about on a quantum computer chip by electric forces which do not disturb the internal quantum states of the strings. According to Wineland and Monroe,
¹⁶
“the resulting architecture would somewhat resemble the familiar charge-coupled device (CCD) used in digital cameras; just as a CCD can move electric charge across an array of capacitors, a quantum chip could propel strings of individual ions through a grid of linear traps.” In 2005, Hensinger, at the University of Michigan, and his team, managed to demonstrate reliable transport of ions “'round the corner” in a T-shaped ion trap array. Since then, even more complicated ion trap CCDs have been developed.

This is an active line of research today at NIST, where the researchers work with beryllium ions. Although the electrodes used to guide the ions in a practicable quantum computer would have to be very small—perhaps as little as 10 millionths of a meter across—Monroe and Wineland emphasize that the engineering involved uses just the same kind of micro-fabrication technologies that are already used in the manufacture of conventional computer chips. Other groups are also working along these lines, undaunted by the need to reduce noise by cooling the electrodes with liquid nitrogen or even liquid helium. But there is another way to combine information from different strings of ions in a quantum computer—using light.

In this approach, instead of using the oscillatory motion of the ions (or ion strings), photons are used to link the qubits together. Ions emit light, and it is possible to set up situations in which the properties of the emitted photons, such as their polarization or their color, are entangled with the internal
quantum states of the ion that is doing the emitting. Photons from two different ions are directed down optical fibers towards a device like the beam-splitting mirrors I described in
Chapter 5
, but working in reverse. With this setup, the photons enter the “splitter” from opposite sides, and are given the opportunity to interact with one another. If they have the same appropriate quantum property (the same polarization, for example), they will interact with one another, become entangled, and leave the beam splitter together along the same optic. But if they have different quantum properties—different polarizations, or different colors, or whatever—they will ignore one another and leave the splitter along different optical fibers. Simple photon detectors placed at the end of each fiber tell the experimenters whether entanglement has occurred or not. Crucially, though, there is no way to determine which ion has emitted which photon; but if the detectors reveal that the photons are now entangled with one another, the ions they came from have also become entangled. Although ion-photon entanglement is tricky to work with, the incentive is that it allows for the possibility of a modular quantum ion processor, built up from many smaller processors linked by photons. Eventually, this could lead to a quantum Internet.

As is so often the case with quantum experiments, most of the time the emitted photons are never gathered up by the beam splitter, and the entanglement does not occur. But, as ever, the solution is simply to keep trying until the experimenters do find photons being detected simultaneously at the appropriate detectors. Once the detectors show that there is entanglement between the two ions—the two qubits—the experimenters also know that manipulating one of
the qubits will affect the other one—the basis of the CNOT gate. This is not just abstract theorizing. A team at the University of Michigan who later moved to the University of Maryland have successfully entangled two qubits in this way in the form of trapped ions separated by a distance of roughly a meter. This is Einstein's “spooky action at a distance” put to practical use.

In these first experiments, the rate at which ion pairs were entangled was only a few per minute. There is a possible way to make the process more efficient by surrounding each ion by highly reflective mirrors, to make what is known as an optical cavity in which photons bounce around before being trapped in an optical fiber. The technology is tricky; but intriguingly it is closely related to the work for which the other half of the 2012 Nobel Prize in physics was awarded, to the Frenchman Serge Haroche, a good friend of Wineland who was born in the same year as him, 1944.

But before I describe the work for which Haroche received the Nobel Prize, a little diversion, into the world of quantum teleportation. It sounds like science fiction, but it is sober science fact; and it turns out to be highly relevant to one of the most promising approaches to making computing with quanta practicable.

THE TELEPORTATION TANGO

Quantum teleportation is based on the spooky action at a distance that so disgusted Einstein but is demonstrated to be real in tests of the EPR “paradox” and measurements of Bell's inequality. It rests on the fact—confirmed in those experiments—that if two quantum entities, let's say two photons, are entangled, then no matter how far apart they are, what
happens to one of those two photons instantly affects the state of the other photon. The key refinement is that, by tweaking the first photon in the appropriate way (called a “Bell-state measurement”), its quantum state can be transferred to the second photon, while the state of the first photon is, of course, changed by being tweaked. In effect, the first photon has been destroyed and the second photon has become what is termed in common parlance a clone of the first photon. Since the original has been destroyed, however, for all practical purposes the first photon has been teleported to the location of the second photon, instantly. It is
not
a duplication process (and it has also been done with trapped ions!).

There's one small catch. In order to complete the transformation, information about the way the first photon was tweaked has to be transmitted to the location of the second photon by conventional means, no faster than the speed of light. This information is then used to tweak the second photon in just the right way (
not
the same way that the first photon was tweaked, but in a kind of reverse process) to complete the transformation. In effect, the conventional signal tells the system what tweak has been applied to photon number one, and the system then does the opposite to photon number two. Quantum teleportation requires both a quantum “channel” and a classical “channel”; it takes two signals to dance the teleportation tango.

A large and successful research effort has gone into making this reality, not least because quantum information offers a way of transmitting information utterly securely using systems that cannot be cracked. I have explained the details in my book
Schrödinger's Kittens
, but the essential point is that information traveling by the quantum “channel” cannot be
read by a third party; in addition, any attempt to eavesdrop will alter the quantum state of the photons, making it obvious that they have been interfered with. This is not the reason why teleportation helps in the design of quantum computers; indeed, in recent times headline-making developments in quantum teleportation have concentrated on much larger scales than those appropriate for computation. But their success emphasizes the reality of the process, and how good scientists now are at working with quanta.

In 2012, two record-breaking experiments made those headlines—both of which will probably have been superseded by the time you read this. First, a large group of Chinese researchers succeeded in teleporting a quantum state through 97 kilometers of open air across Qinghai Lake, using a telescope to focus the photons. Almost as an aside, the experiments confirmed the by-now-expected violation of Bell's inequality, offering insight for the theorists into the foundations of quantum physics. A few weeks later, a team from Austria, Canada, Germany and Norway teleported the properties of a photon across a distance of 143 kilometers, from the astronomical observatory at La Palma, in the Canary Islands, to a European Space Agency ground station on the neighboring island of Tenerife. Both the transmitting station and the receiving station were located roughly 2,400 meters above sea level, where the air is thin and atmospheric interference is reduced.